The answer is: You can't. You can make all manner of approximations and send them an @ message (public) or a mail (not Twitter), but you can't send them a DM, unless they follow you. It's a privacy feature, else every miscreant out there could just flood your essentially private DM box without your permission.

Ryan Dube

July 15, 2010 at 6:22 pm

Yes! One excellent option is using TweetToEmail to do this...and you can set up multiple friends who may not have Twitter accounts. Great service for exactly what you want to do.

If you were just referring to sending a message to someone who doesn't follow you, then definitely @username works and they don't need to be following you to receive it.

Swilliam82

July 1, 2010 at 4:55 pm

Open the list 'Following' and then click on the profile you want to send direct massage, you see options; un-follow, send direct massage, retweet and etc.
From here you can easily send massages to those and ask about your tweets. Thanks